In this paper, we study the stochastic maximum principle for optimal control prob- lem of anticipated forward-backward system with delay and Lovy processes as the random dis- turbance. This control system can be described by the anticipated forward-backward stochastic differential equations with delay and L^vy processes （AFBSDEDLs）, we first obtain the existence and uniqueness theorem of adapted solutions for AFBSDEDLs; combining the AFBSDEDLs＇ preliminary result with certain classical convex variational techniques, the corresponding maxi- mum principle is proved.
The pricing and hedging problem of foreign currency option with higher borrowing rate is discussed.The method to obtain the price and hedging portfolio of currency option is based on backward stochastic differential equations(BSDE for short) theory and Malliavin calculus technique.The sensitivity of the model parameters is also considered and some numerical simulations are given to illustrate our conclusion.
